Find HCF and LCM-: 1-x^2 and x^3-1?

Question

i know that its HCF is x-1 and LCM is (x^3-1) (x+1) but i want to know that in the solution we take - common but when we find LCM why we do'nt take - in the answer.

Answer 1

1 - x^2 = -(x + 1)(x - 1)
x^3-1 = (x - 1)(x^2 + x + 1)
GCF = x - 1
LCM = (x - 1)(x^2 + x + 1)(x + 1)
LCM = -(1 - x)(x^2 + x + 1)(x + 1)

Answer 2

factorize each term
1-x^2 = -(x-1)(x+1)
x^3-1 = (x-1)(x^2+x+1)

for HCF take the common term x-1

for LCM take each term with higest power in each expression

= (x-1)(x+1)(x^2+x+1)

(the reason is that each expression should devide LCM)